In the development of this invention the performances of several data association algorithms under high clutter operating conditions was explored. The algorithms studied included: nearest neighbor standard filter (NNSF), probabilistic data association (PDA), and joint probabilistic data association (JPDA). After observing the initial results from the simulation, this novel data association algorithm, referred to herein as the Hicks' Probabilistic Data Association (HPDA). This new HPDA algorithm was tested and compared with prior other algorithms and found to be superior under various operating conditions.
A Monte-Carlo simulation was executed for the three algorithms. The performance of each was evaluated by two methods. First, the average fraction of tracks lost was determined. A track is the computer predicted path of a target, and was declared lost when its position error exceeded the gate threshold by a specified threshold. The number of trials was chosen to yield a confidence of .+-.0.05. The second measure of effectiveness was the RMS position error. Once a track was declared lost, it was no longer used to calculate the RMS position error.
The Monte-Carlo simulations yielded some interesting results. The performances of PDA and NNSF crossed as the clutter density was increased, with NNSF having the better performance under dense clutter conditions. The explanation for this varying performance lies in the fact that there are two elements which control the performance of the algorithms.
The first characteristic of this simulation is the crossing target performance. NNSF uses a hit or miss type approach. It chooses the closest measurement and uses it to update the state. With two crossing targets it will be incorrect half of the time. JPDA on the other hand uses all of the measurements to form a weighted average which is then used to update the target's state. At point certain points, the measured target positions of two crossing aircraft may be too close for a clear distinction to be made between the two. JPDA uses a weighted average of the two measurements to update each target's state. This causes both tracked target positions to be very close until a point where a larger separation occurs. At such point, the measured target positions have separated enough for the tracker to make a clear distinction between the two targets, and then, the tracked positions begin to closely follow the true tracks. This results in improved performance in tracking crossing targets.
The other characteristic of this simulation is the high clutter performance. NNSF picks a single measurement to be used to update the state, and is either right or wrong. The probability that it is incorrect goes up linearly with increased clutter density. JPDA, however, uses all of the information to update the state, and under high clutter conditions, most of that information is incorrect. This leads to a rapid non-linear decay in performance which quickly decays further than NNSF.
By considering the joint likelihood of every measurement being associated with each target, it was hoped that a better decision could be made about which measurement should be attributed to each target. This should improve the crossing target performance, while avoiding the non-linear performance degradation.